Practice: Calculate the standard deviation for the following results: 0.039, 0.061 and 5.3 x 10** ^{-2}**.

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**Standard deviation** measures how close our numerical data points are to one another and to the “true” value.

Concept #1: Understanding Standard Deviation

**Transcript**

We're going to say that the standard deviation, so standard deviation, measures how close data results are to the mean or average value. We're going to say sometimes it's easy for us to look when we have a few numbers. We just simply look to see how close they are to one another, how close they are to the true value. But sometimes, we may require some help. That's the whole basis for standard deviation.

This is going to become an important idea when it comes to accuracy and precision in this chapter and also when you take your lab. Because when you're doing labs, labs are all based on how accurate and how precise can your measurements be when doing any of the experiments that you have to do.

We're going to say here, the equation for standard deviation is the square root, where we have the summation. This is sigma, the summation of x1 minus x squared divided by n minus one. We're going to say that x or x1 is simply a measurement. We're going to say that x with a bar on top of it is our mean or average of all the measurements added up and divided by the total number of measurements. This is our mean or average. Then we're going to say n, n represents the number of measurements that we have.

The equation might seem a little bit intimidating, but it's really easy as long as you can remember what it is and how do we plug in the numerical values that were given.

Example #1: Calculate the standard deviation for the following results: 5.29, 5.35 and 5.31.

Practice: Calculate the standard deviation for the following results: 0.039, 0.061 and 5.3 x 10** ^{-2}**.

0 of 3 completed

Concept #1: Understanding Standard Deviation

Example #1: Calculate the standard deviation for the followi...

Practice #1: Calculate the standard deviation for the follow...

A student determined the percent water in a sample. In four trials, values of 16.145%, 16.160%, 16.156%, and 17.279% were obtained for the percent water in sample. What value should be used for the reported percent water?
(A) 16.154%
(B) 16.435%
(C) 16.145%
(D) 17.279%

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows:1. 22.52, 22.48, 22.542. 22.64, 22.58, 22.62(b) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Find the weighted average of these values.Value Weight1 75%2 15%3 10%

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows:1. 22.52, 22.48, 22.542. 22.64, 22.58, 22.62(a) Calculate the average percentage for each set of data, and state which set is the more accurate based on the average.

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